\[ {}y^{\prime \prime }-y = t^{2} \]

\[ {}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right ) \]

\[ {}L i^{\prime }+R i = E_{0} \delta \left (t \right ) \]

\[ {}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi } \]

\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \]

\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \]

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+t -1, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )-5 t -2] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 t +2, y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )-8 t -8] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )] \]

\[ {}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\sqrt {2}\, y \left (t \right ), y^{\prime }\left (t \right ) = \sqrt {2}\, x \left (t \right )-2 y \left (t \right )\right ] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-4 t +1, y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )+3 t +4] \]

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+t -2] \]

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = -x \left (t \right )-5 y \left (t \right )+t +1] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = t y \left (t \right )+1, y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )] \]

\[ {}y^{\prime } = y^{2}-x \]

\[ {}y^{\prime } = y^{2}-x \]

\[ {}y^{\prime }-2 y = x^{2} \]

\[ {}y^{\prime }-2 y = x^{2} \]

\[ {}y^{\prime } = y+x \,{\mathrm e}^{y} \]

\[ {}y^{\prime } = y+x \,{\mathrm e}^{y} \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

\[ {}y^{\prime \prime }-x y = 0 \]

\[ {}y^{\prime \prime }+x^{2} y = 0 \]

\[ {}y^{\prime \prime }-2 x y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \]

\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

\[ {}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0 \]

\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \]

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

\[ {}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \]

\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0 \]

\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \]

\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }-x y = 1 \]

\[ {}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x} \]

\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \]

\[ {}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0 \]

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }+y \cos \left (x \right ) = 0 \]

\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \]

\[ {}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0 \]

\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0 \]

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0 \]

\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \]

\[ {}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

\[ {}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0 \]

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (5+x \right ) y = 0 \]

\[ {}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (-3+x \right )^{2} y^{\prime }-y \left (1+x \right ) = 0 \]

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0 \]

\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \]

\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \]

\[ {}x y^{\prime \prime }+y^{\prime }+10 y = 0 \]

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

\[ {}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0 \]

\[ {}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0 \]